Retention mechanism, isocratic and gradient-elution ...distribution, liquid chromatography under...

Journal of Chromatography A, 869 (2000) 65–84www.elsevier.com/ locate /chroma

Retention mechanism, isocratic and gradient-elution separation andcharacterization of (co)polymers in normal-phase and reversed-phase

high-performance liquid chromatography* ˇ ´ˇ ´Pavel Jandera , Michal Holcapek, Lenka Kolarova

´ ´Department of Analytical Chemistry, University of Pardubice, Nam. Legiı 565, 532 10 Pardubice, Czech Republic

Abstract

Synthetic (co)polymers or (co)oligomers with two (or more) repeating groups show not only molar mass distribution, butalso composition and sequence distribution of the individual repeat units. To characterize such two- (or more-) dimensionaldistribution, liquid chromatography under ‘‘critical conditions’’ has been suggested, where the separation according to onetype of repeating units is suppressed by balancing the adsorption and the size-exclusion effects. In present work it is shownthat by combination of adequately selected separation conditions in normal-phase and in reversed-phase systems, thetwo-dimensional distribution mode can be adjusted to result in the separation following the distribution of any of the tworepeat units in ethylene oxide–propylene oxide block (co)oligomers. Based on the retention mechanism suggested, predictionand optimization of the conditions for isocratic and gradient-elution separations of (co)oligomers is possible. HPLC–MSwith atmospheric-pressure chemical ionization is a valuable tool for unambiguous identification of the individual(co)oligomers and their tracking in course of method development. Gradient elution can be used for the separation andcharacterization of block (co)oligomers of ethylene oxide (EO) and propylene oxide (PO) according to the number of theunits in one block, while the separation according to the distribution of the units in the other block is suppressed. The effectsof the arrangement of the individual EO and PO blocks in the block (co)oligomers (the sequence distribution) affectssignificantly the retention behavior and the selection of the optimum separation conditions. 2000 Elsevier Science B.V.All rights reserved.

Keywords: Gradient elution; Retention mechanism; Polymers; Ethylene oxide; Propylene oxide

1. Introduction controls their quality and suitability for specificapplications. For the evaluation of the quality of

With widespread use of synthetic polymer- or technical products and for further development ofoligomer-based materials in industry, agriculture and polymerization techniques leading to new tailor-households, the demands increase on the properties made materials with improved properties, characteri-of technical products with respect to mechanical and zation methods are necessary to provide informationchemical resistance, biodegradability, etc. Technical on the polymer structure. In addition to classical wetpolymers and oligomers contain varying types and analytical and spectroscopic methods, separationnumbers of structural units, the distribution of which techniques and especially size-exclusion (SEC) and

high-performance liquid chromatography (HPLC)can provide most detailed information on the com-*Corresponding author. Tel.: 1420-40-603-7023; fax: 1420-40-

603-7068. position of the polymer products.

0021-9673/00/$ – see front matter 2000 Elsevier Science B.V. All rights reserved.PI I : S0021-9673( 99 )01216-9

66 P. Jandera et al. / J. Chromatogr. A 869 (2000) 65 –84

The basic information on the character of synthetic ous distribution types can be characterized usingpolymers and oligomers is their molecular mass. HPLC in normal-phase and in reversed-phase modesHowever, technical products never are a pure single (interaction chromatography).species, but are more or less complex mixtures of Ethylene oxide–propylene oxide (EO–PO) blockdifferent compounds containing one or more struc- copolymers are nonionic surfactants frequently usedtural repeat units. The composition of these mixed in washing machines. Because of their thickeningproducts can be characterized by one or more types capacity and low skin sensitivity they found alsoof distribution. applications as the emulsifiers and solubilizers of

(1) Oligomers or polymer products composed of a flavors and fragrances in cosmetic products.single repeat monomeric unit, U, are always mixtures The oxypropylene chain –[CH –CH(CH )–O] –2 3 m

containing individual species with various numbers 5(PO) in the EO–PO block copolymers is hydro-m

of repeat units, n. The distribution of the species with phobic, but the oxyethylene chain –[CH –CH –2 2

different numbers of the repeat units represents the O] –5(EO) is hydrophilic. Two types of blockn n

molecular mass distribution in the product, which (co)polymers with different sequence distribution cancan be schematically represented as: be prepared using different technologies: The

(EO) –(PO) –(EO) type is prepared by ethoxyla-n m n–U–, –U–U–, –U–U–U–, –U–U–U–U–, tion of polypropylene glycol. The reversed reaction–U–U–U–U–U–, . . . sequence, reaction of polyethylene glycol with pro-

pylene oxide is used to prepare the second type of(2) Some polymers may contain various end block (co)polymers, (PO) –(EO) –(PO) . All threem n m

groups, E , E , . . . so that the functionality type types of distribution – the molecular mass distribu-1 2

distribution can be attributed to such products, e.g.,: tion, the chemical composition distribution and thesequence distribution – affect the properties of the

E –U–U–U–U–E , E –U–U–U–U–E ,1 1 2 2 technical products. With increasing average molecu-E –U–U–U–U–E lar mass the gelation becomes easier, whereas in-1 2

creasing number of PO units improves the wetting(3) (Co)polymers and (co)oligomers contain two properties of the products and increasing number of

or more different monomeric repeat units, U , EO units improves the solubility in water, but1

U , . . . in various ratios, n :n . . . , controlling the impairs the wetting properties. The (co)polymers2 1 2

chemical composition distribution of the product, with the (PO) –(EO) –(PO) structure are char-m n m

schematically represented as: acterized by reduced foam formation and gelationwith respect to the (co)polymers of the (EO) –n–U –U –U –U –U –, –U –U –U –U –U –,1 2 1 1 1 1 2 1 2 1 (PO) –(EO) type [1].m n

–U –U –U –U –U –, –U –U –U –U –U –1 2 2 1 2 1 2 2 2 2 Efficient separations of ethoxylated non-ionic sur-factants can be achieved by HPLC both in normal-

(4) Finally, different monomeric units can be phase systems on columns packed with unmodifiedpresent in different sequences of microblocks with silica gel or with amino, nitrile or diol chemicallydifferent numbers of the individual repeat units along bonded phases [2–16] and in reversed-phase systemsthe polymer chain in random or block (co)polymers. [17–26]. Few reports have been published so far onThis polymer heterogeneity is characterized by the the systematic investigation of their retention be-sequence distribution, such as: havior [27,28].

Individual ethoxylated oligomers are eluted in the–U –U –U –U –U –U –,1 2 1 2 1 2order of increasing number of oligomeric oxy-

–U –U –U –U –U –U –,1 1 1 2 2 2 ethylene units in normal-phase systems. In reversed-–U –U –U –U –U –U – phase systems, the order of elution of the oligomers1 1 2 2 2 1

depends on the oligomeric series and on the mobileThe molecular mass distribution can be deter- phase. For example, oligoethylene glycol phenyl

mined by size-exclusion chromatography, but vari- ethers are eluted in the order of increasing number of

P. Jandera et al. / J. Chromatogr. A 869 (2000) 65 –84 67

oxyethylene units on an octadecylsilica column [29] sample compounds are retained because of theand so are oligoethylene glycol octylphenyl ethers on interactions with the stationary and (or) with thea trimethylsilica column in mobile phases comprised mobile phase. If the three HPLC modes are appliedof water and methanol [24], whereas oligoethylene to polymer separations, they can be classified asglycol nonylphenyl ethers are almost unseparated on interaction chromatography to be distinguished froma C column in these mobile phases (Fig. 7 in Ref. SEC. If size- or ionic-exclusion effects are absent in18

[30]) and their order of elution is reversed in interaction chromatography, all analytes are elutedaqueous acetonitrile [26,31,32], propanol or dioxane with elution (retention) volumes V 5V greater thane R

[30], like in chromatography on a mixed-mode V and are limited only by the acceptable time ofM

reversed-phase / ion-exchange column [33]. We have analysis. Hence, the separation selectivity for thestudied earlier simultaneous effects of the degree of species with different numbers of oligomeric unitspolymerization, n, and of the concentration of the (the oligomeric selectivity) is usually greater than instronger solvent in binary mobile phases on the SEC. The retention of polymers and oligomers inretention in nonionic oligomeric series, both in interaction chromatography depends on the numberreversed-phase [30,34], and in normal-phase [35] of repeat units, n, and on the concentration of thesystems. Recently, we have extended this inves- strong eluent, w, in the mobile phase. The retentiontigation to the anionic oligomeric surfactants in characterized by the retention factors, k5(V 2V ) /R M

reversed-phase [36] and normal-phase ion-pair sys- V , usually increases so that the logarithms of theM

tems [37] and to ethoxylated alcohol surfactants with retention factors change in a linear manner as thedifferent numbers of oxyethylene units and alkyl number of repeat units, n, i.e., the molecular mass,chain lengths [38]. M increases [30].r

In the present work, we investigated possibilities In reversed-phase systems, the logarithms of theof using HPLC in normal-phase and in reversed- retention factors usually decrease in a linear mannerphase modes for the determination of the molecular with increasing concentration of the organic solventmass distribution, chemical composition distribution (stronger eluent, B) in a binary aqueous–organicand block sequence distribution in block copolymers, mobile phase, w

with special attention to the EO–PO block copoly-log k 5 a 2 mw (1)mers.

The dependence of k on the number of repeatunits, w, and on n can often be described by Eq. (2)2. Theoretical[30,34]:

SEC has been widely used for the characterization log k 5 a 1 a n 2 (m 1 m n)w (2)0 1 0 1of the molecular mass distribution. In the separationscontrolled solely by size-exclusion mechanism, poly-

In normal-phase systems with binary organicmeric compounds, dependent on their size, partlymobile phases containing two solvents, one lesspenetrate into the pores of the inert column packing.polar (A) and the other more polar (B), the depen-As the volume of the pores accessible to the mole-dence of the retention factors on the concentration wcules decreases as the size of the molecules in-of the solvent B can be often described by a simplecreases, the elution volumes, V , decrease withe Eq. (3) [35]:increasing molecular masses of the individual species

and V of all sample components are in the rangee log k 5 a 2 m log w (3)between the column interparticle volume, V , and thei

column hold-up volume, V , so that the volume of (this equation formally applies also in HPIEC, whereM

the eluate available for the separation is rather w is the concentration of a salt, acid or base in anlimited. aqueous or aqueous–organic mobile phase).

In reversed-phase (RP) HPLC, in normal-phase In some normal-phase systems, Eq. (3) fails to fit(NP) HPLC and in ion-exchange HPLC (HPIEC), all the retention data and a three-parameter Eq. (4)


should be used to describe adequately the retention V 5V 1 K V 1 K V (6)e i sec p i s

behavior [39]:where V is the interstitial volume (volume outsidei

the particles in the column), V is the pore volume in1 p]]]k 5 (4)m the column and V is the volume of the stationarys(a 1 bw)

phase, K and K are the distribution constants forsec i

size exclusion and for the retention equilibriumFor NP systems where Eq. (3) applies, the depen-between the stationary and the mobile phases.dence of k on n and on the concentration of a more

Exact compensation of the size-exclusion effectspolar solvent B, w, in a mobile phase comprised ofand of the interactions causing the retention in thetwo organic solvents with different polarities can bestationary phase for oligomers with different num-described by Eq. (5), formally similar to Eq. (2)bers of repeat units should result in the elution of all[27,35]:oligomers close to the column hold-up volume (noexclusion and no retention). The size-exclusionlog k 5 a 1 a n 2 (m 1 m n) log w (5)0 1 0 1effects may influence also the behavior of retainedcompounds, but the interaction effects predominate.where a , a , m , m in Eqs. (2) and (5) are0 1 0 1The size-exclusion effects may either influence theconstants depending on the character of the repeatvalues of the constants a , a , m , m of Eqs. (2) and0 1 0 1units and of the end groups in the oligomer or(5) or – possibly – may contribute to non-linearitypolymer, on the chemistry of the stationary phase orof the log k versus n plots.of the adsorbent in the column and on the type of the

From Eqs. (2) and (5) it follows that co-elutionmobile phase components, but are independent of thecan occur also in pure retentive interaction-controlledconcentrations of the mobile phase components. Forseparations at a certain concentration of the com-some chromatographic systems and oligomericponent B, w in the mobile phase if:iseries, additional terms, quadratic with respect to n

or w, should be added to the right-hand side of Eqs. either: w 5 a /m (RP systems) ori 1 1(2) or (5).a / m1 1w 5 10 (NP systems).In liquid chromatography of polymers on a porous i

active column packing, size-exclusion effects andinteractions with the stationary (and with the mobile) If the contribution of each repeat unit [such as POphases can affect simultaneously the chromatograph- and EO in EO–PO (co)oligomers] to the retentionic behavior. Sometimes conditions can be found at energy of copolymers is constant, the dependence ofwhich the size-exclusion effects exactly compensate the retention of the individual species on the numberthe interactions of the polymers with the components of the two units, n and n , can by described Eq.EO PO

of the chromatographic system [40–42], so that (7):individual polymers or oligomers with different

2log k 5 log b 1 n log a 1 n log gnumber of repeat units are co-eluted in a single peak EO EO EO EO

2at the same elution volume, V independent of n.e 1 n log a 1 n log g (7)PO PO PO POThese conditions are known as ‘‘liquid chromatog-raphy at the critical point of adsorption’’ or as the Here, a and a express the oxyethylene and theEO PO

‘‘point of exclusion–adsorption transition’’ and have oxypropylene separation selectivities, respectively,been recently reviewed [43]. Recently, Thrathnigg et i.e., the elution ratio of the oligomers differing byal. have presented theoretical explanation of the one oxyethylene or oxypropylene oligomeric repeatbehavior of lower [44] and of higher [45] poly- unit, log b represents the contribution to the re-ethylene glycol ethers in reversed-phase systems by tention by the end group(s) and log g the deviationscombined effects of adsorption and size exclusion. of all kinds from the linear log k versus n plots, i.e.,

The elution volume, V , contributed to by both from the Martin rule (for more details see Refs. [34]e

size-exclusion effect and interactions causing the and [46]). The dependence of the retention andretention in the stationary phase can be expressed as: separation selectivity of the individual block units


can be described by equations similar to Eqs. (2) and chromatographic separations of complex mixtures of(5) in reversed-phase and in normal-phase systems, (co)oligomers with bimodal distribution should berespectively. theoretically possible – the separation into groups

The conditions for co-elution of oligomers with with the same number of polar units and withdifferent numbers of a certain type of repeat unit different less-polar units in reversed-phase systems,have been employed for the separation of various or into groups with the same number of non-polarpolymers according to their functionalities. The units, but with different numbers of more polar units‘‘critical conditions’’ are especially useful for charac- in normal-phase systems.terization of block copolymers which represent very LC–MS techniques are particularly useful for thecomplex mixtures of individual species. To facilitate analysis of (co)polymers and (co)oligomers, as theythe analysis, the separation of one block is intention- allow mass spectral identification of individual oligo-ally suppressed to make possible the analysis of the mers in the groups separated by HPLC under con-other block with respect to its molar mass dis- ditions close to ‘‘critical’’ [38,50,51], so that two-tribution [47]. This method has been applied to dimensional separations are not necessary. Off-linevarious polymers and oligomers, including poly- coupling with fast atom bombardment (FAB) orethylene glycol ethers. Reversed-phase chromatog- desorption chemical ionization was originally usedraphy with acetonitrile–water [48] or with methanol– for LC–MS of surfactants [52]. Later, direct on-linewater [49] mobile phases was employed for this coupling was possible using new interfaces based onpurpose. different ionization techniques such as continuous

If Eq. (2) in RP systems or Eq. (5) in NP systems flow FAB [53,54], thermospray or electrospraycontrol the retention of the individual blocks in the [55,56]. In an earlier work [38], we applied LC–MSblock copolymers, the separation solely according to with atmospheric pressure chemical ionizationthe distribution of one type, i, of repeat units can be (APCI) for the investigation of retention mechanismachieved if the deviations from the Martin rule are of oligomers with bimodal distribution of alkyls andnot very significant, i.e., if g ¯1 and if: of EO groups in samples of ethoxylated alcohols ini

normal- and reversed-phase systems.w 5 a /m (for Eq. 2 in the RP systems) ori i i

a / mi iw 5 10 (for Eq. 5 in the NP systems)i

In chromatography of polymers, isocratic elution 3. Experimentalallows separation of a limited number of compoundsand gradient elution is necessary for the separation ofmore complex samples. To accomplish gradient-elu- 3.1. Materialstion separation of block copolymers according to asingle distribution mode for one type of oligomer n-Hexane and dichloromethane were obtainedunits and close to ‘‘critical conditions’’ for the from Baker (Deventer, The Netherlands), acetonitrilesecond block, the oligomer selectivity for the second and 2-propanol from Labscan (Dublin, Ireland). Alltype of oligomer units, a , should not depend solvents were of HPLC grade. Water was doubly2

significantly on the composition of the mobile phase, distilled in glass (with addition of potassium per-i.e., m ¯0. manganate and sodium hydrogencarbonate). Glass1

The identification of the individual compounds in cartridge columns (15033 mm I.D.), packed withthe chromatograms of products containing Separon SGX C , particle size 7 mm (octadecyl18

(co)oligomers with two different distribution modes silica) and Separon SGX NH , 7 mm (aminopropyl2

can be difficult if each mode contributes to the silica), both average pore size 8 nm, were purchasedretention. In normal-phase systems, polar repeat units from Tessek, Prague, Czech Republic.contribute more strongly to the retention than the less Technical samples of EO–PO block copolymers

´polar oligomer units and the effect is opposite in were obtained from Sloveca (Novaky, Slovak Re-reversed-phase systems. Hence, two-dimensional public): Slovank 310, (EO) –(PO) –(EO) type,n m n


Novanik 600/20, 600/40 and 600/50, (PO) – Mild ionization conditions with cone voltage of 10 Vm

(EO) –(PO) type, with different average numbers were selected to suppress the fragmentation.n m

of EO and PO units. Each experiment was repeated at least twice. Fromthe retention volumes, V , the retention factors, k5R

(V /V 21) were determined. The column hold-upR M

3.2. Chromatographic and mass spectrometric volumes, V , were determined as the elution volumesM

instrumentation of non-retained compounds (methanol and acetoni-trile for a Separon SGX C column, V 50.74 ml18 M

The liquid chromatograph used consisted of a and n-hexane for a Separon SGX Amine column inModel 616 pump, a Model 7171 autosampler, a normal-phase systems, V 50.90 ml) and both VM R

four-channel solvent delivery system (low-pressure and V were corrected for the volumes of theM

gradient system), a thermostatted column compart- connecting tubing. Each chromatographic peak wasment, a Model 996 photodiode-array detector and a attributed to the individual oligomer species on the

1Millenium chromatography manager (all from Wa- basis of the mass of its [M1H] ion in the APCI1 1ters, Milford, MA, USA). As the sample compounds mass spectrum. Peaks of the [M1H] , [M1Na]

1do not absorb significantly in the UV region, the and [M1K] ions were identified as the mostoutlet from the column was connected either to a significant peaks in the mass spectra. From their m /zModel PL-EMD 950 evaporative light scattering values, corresponding combinations of the numbersdetection (ELSD) system (Polymer Labs., Shrop- of the oxypropylene (–CH –CH(CH )–O–, PO) and2 3

shire, UK) or directly to a VG Platform quadrupole oxyethylene (–CH –CH –O–, EO) groups in the2 2

mass analyzer (Micromass, Manchester, UK) with individual oligomers were determined. With the coneatmospheric pressure chemical ionization in the voltage of 10 V, the fragmentation is negligible.positive mode, molecular mass range up to 3000. From the total ion current (TIC) chromatograms, theThe ELSD signal was processed using a Vectra V12 chromatograms corresponding to the species with apersonal computer (Hewlett-Packard, Avondale, CA, constant number of oxyethylene but different num-USA) with a CSW 1.6 chromatographic data station bers of oxypropylene units or to the species with a(Data Apex, Prague, Czech Republic). constant number of oxypropylene but different num-

bers of oxyethylene units were reconstructed select-ing only the ion currents of the corresponding [M1

13.3. Procedures H] ions.Multiparameter nonlinear regression analysis using

Mobile phases for isocratic experiments were the ADSTAT software (TRILOBYTE, Prague,prepared by pre-mixing appropriate volumes of Czech Republic) was used to calculate the constantssolvents, filtered through a 0.45-mm Millipore filter of the dependencies of log k on the numbers ofprior use and degassed by continuous stripping with oxyethylene and oxypropylene units (Eq. (7)). Thehelium during the analysis. The samples were pre- constants of this equation are given in Tables 1, 3pared by dissolving in the mobile phase in con- and 5 separately for the (EO) –(PO) –(EO) andn m n

centrations ca. 1 mg/ml. The column temperature (PO) –(EO) –(PO) block copolymer types in them n m

was kept at 408C and the flow-rate at 1 ml /min in all three chromatographic systems studied. Linear orexperiments. A 10- or 20-ml sample volume was nonlinear regression was used to determine theinjected into the liquid chromatograph. parameters of the equations describing the depen-

Mass spectrometric data were acquired in the dence of the retention factors on the composition ofmolecular mass range from 35 to 1500 at the scan the mobile phase, which are listed in Table 2 for theduration of 1.9 s in the positive-ion APCI mode. A Separon SGX C /acetonitrile–water RP system18

potential of 3.05 kV was applied on the discharge (Eq. (1)), in Table 4 for the Separon SGX Amine/2-needle. The temperature was held at 5008C in the propanol–n-hexane and in Table 6 for the SeparonAPCI probe and at 908C in the ion source. Nitrogen SGX Amine/acetonitrile–water–dichloromethanewas used as the drying, sheath and nebulizing gas. NP systems (Eq. (4)).


Table 1Constants of the dependences of the retention factors, k, on the number of oxyethylene, n and oxypropylene, n , repeat units ofEO PO

(PO) –(EO) –(PO) (Novanik) and (EO) –(PO) –(EO) (Slovanik) block copolymers on a Separon SGX C column in acetonitrile–m n m n m n 182 2water mobile phases: log k5log b 1n log a 1n log g 1n log a 1n log gEO EO EO EO PO PO PO PO

50% CH CN 60% CH CN 70% CH CN 80% CH CN 90% CH CN3 3 3 3 3

NovanikLog b 21.2660.02 21.7260.08 20.4060.05 20.2460.02 0.560.1Log a 20.001160.0004 0.000560.0003 0.000360.0001 0.0000960.00006 20.000660.0005EO

Log a 0.18760.005 0.2260.02 0.0160.01 20.02160.005 20.0460.04PO

Log g 20.001260.0003 20.00460.001 0.004460.0008 0.004460.0003 0.00260.003POaC.D. 0.9995 0.9914 0.9868 0.9945 0.8723

SlovanikLog b 21.19360.008 21.0560.02 20.83960.005 20.76460.004 20.57060.006Log a 20.02560.004 20.0260.01 20.02660.002 20.01960.002 0.00160.003EO

Log g 0.003960.0009 0.00160.002 0.001860.0006 0.003060.0005 0.004060.0007EO

Log a 0.177160.0006 0.14760.001 0.111260.0003 0.082660.0003 0.06360.003POaC.D. 0.9996 0.9967 0.9996 0.9995 0.9985

a C.D.5Coefficient of determination.

4. Results and discussion overlapped peaks of the (EO) –(PO) –(EO)n m n

(Slovanik, Fig. 1A) and the (PO) –(EO) –(PO)m n m

4.1. HPLC–APCI-MS analysis of the EO–PO (Novanik, Fig. 1B) (co)oligomers, in which series ofblock (co)oligomers peaks with different EO or PO numbers are apparent

at characteristic m /z values.Mass spectrometric detection with APCI ioniza- By selecting the ions corresponding to a series

tion in the positive ion mode allows sensitive with a single EO unit and with different numbers ofdetection of the samples of EO–PO (co)oligomers, PO units, or the ions corresponding to a series with awhich do not absorb radiation in the UV region. single PO unit and with different numbers of EOFurther, unambiguous identification of the individual units, chromatograms corresponding to the individualspecies is possible even in the chromatograms with oligomer units distribution modes were extracted, sooverlapping peaks, as the ionization conditions (sam- that overlapping peaks could be deconvolved. In theple cone voltage) were adjusted to yield only [M1 chromatograms reconstructed in this way, retention

1H] ions. Fig. 1 shows examples of mass spectra of volumes could be determined for the investigation of

Table 2Constants of the dependences of the retention factors, k, of (EO) –(PO) –(EO) (Slovanik) block copolymers on the concentration ofn m n

22acetonitrile, w (%, v /v, ?10 ), on a Separon SGX C column in acetonitrile–water mobile phases (50–80% acetonitrile): log k5a2mw18

(n 52) n 511 n 512 n 513 n 514 n 515EO PO PO PO PO PO

a 1.7960.06 2.1160.05 2.4260.05 2.7460.02 3.0660.01m 2.0760.09 2.3960.07 2.6660.08 2.9760.04 3.2760.02

ak 0.9960 0.9983 0.9981 0.9997 0.9999

(n 513) n 50 n 51 n 52 n 53 n 54PO EO EO EO EO EO

a 2.4560.05 2.4360.04 2.4260.05 2.4260.02 2.4060.04m 2.6660.08 2.6560.05 2.6660.08 2.6960.03 2.6760.06

ak 0.9983 0.9992 0.9981 0.9997 0.9990a k5Correlation coefficient.


Fig. 1. APCI(1) mass spectra of coeluted peaks of EO–PO block copolymers; Column: Separon SGX C , gradient 15–100% acetonitrile18

in water in 25 min (0.5 ml /min, 408C). Peaks are marked for series of [M1H]1 ions with various numbers of EO and PO units: (A)(PO) –(EO) –(PO) (Novanik); n 51, n 510–17 (j); n 52, n 58–17 (d); n 53, n 57–16 (s) and n 54, n 57–14 (h).m n m PO EO PO EO PO EO PO EO

(B) (EO) –(PO) –(EO) (Slovanik); n 50, n 511–20 (j); n 51, n 511–19 (h); n 52, n 511–18 (d) and 4 n 53,n m n EO PO EO PO EO PO EO

n 511–17 (s).PO

the effects of the chromatographic conditions on the 4.2. Effect of the molecular mass and chemicalseparation. Further, peak areas in the deconvolved composition distribution on the retention behaviorchromatograms can be integrated and the distribution of the EO–PO block (co)oligomersof the EO and PO units among the individual speciescan be determined. In the reversed-phase systems studied, i.e., on a


Separon SGX C column with acetonitrile–water18

mobile phases, the retention of both the (EO) –n

(PO) –(EO) (Slovanik) and the (PO) –(EO) –m n m n

(PO) (Novanik) (co)oligomers can be described bym

Eq. (7). The constants of this equation are given inTable 1. The quadratic terms with log g areEO

negligibly small for the Novanik samples and thequadratic terms with log g for the SlovanikPO

samples. The quadratic terms with log g for theEO

Slovanik samples and with log g for the NovanikPO

samples are more significant, but are one- to two-orders of magnitude smaller than the linear terms andcan be neglected to first approximation, as it isdemonstrated by the log k versus n and n plotsEO PO

in Figs. 2 and 3, which are close to straight lines.The oligomer selectivity for rather polar EO units

is low in the reversed-phase systems studied (theterm log a is approximately two-orders of mag-EO

nitude lower than the oligomer selectivity for lesspolar PO units, log a ). For reversed-phase systemsPO

the retention (log k) increased in linear manner withincreasing number of the repeat PO oligomer units,n , so that these systems are principally well suitedPO

for the separations of the EO–PO (co)oligomersaccording to the number of PO units. The (EO) –n

(PO) –(EO) (Slovanik) (co)oligomers could bem n

separated according to the number of PO units in allmobile phases studied, but the (PO) –(EO) –(PO)m n m

(Novanik) (co)oligomers only in mobile phases with60% or less acetonitrile. The oligomer selectivitiesfor PO units in the Slovanik and Novanik samplesare approximately equal to each other in 50%acetonitrile as the mobile phase. With the Slovaniksamples, log a regularly decreases with decreasingPO

concentration of acetonitrile in the mobile phaseFig. 2. Dependencies of the retention factors, k, on the number of

from 50 to 90%. (Table 1). On the other hand, the PO units, n , for the oligomers with two EO units (A) and on thePOdependence of the oligomer selectivity for PO units number of EO units, n , for the oligomers with 13 PO units (B)EO

in the Novanik samples is more complex. There is in a Slovanik sample, type (EO) –(PO) –(EO) . Column:n m n

Separon SGX C , mobile phase: acetonitrile–water (50:50) (1),little difference between the log a values in 50 and 18PO(60:40) (2), (70:30) (3), (80:20) (4), (90:10) (5), temperature:60% acetonitrile, but the oligomer selectivity for the408C.

PO units is much lower in mobile phases with 70 and80% acetonitrile and reversed elution order is ob-served for the oligomers with different numbers ofPO units in 90% acetonitrile (line 5 in Fig. 3A). We (co)oligomers, the inner block is formed by the EOhave observed earlier similar retention behavior as units and the end blocks by the PO units, whereaswith the Novanik samples for ethoxylated fatty the EO and the PO blocks in the Slovanik samplesalcohol surfactants with two blocks of different are arranged in the opposite order. The sequencepolarities – (EO) and (CH ) [38]. In the Novanik distribution in the EO–PO (co)oligomers affectsn 2 m


for the EO units is close to zero in the whole rangeof the mobile phase composition tested (Figs. 2B and3B). However, the oligomer selectivity for the EOunits is one- to two-orders of magnitude lower forthe Novanik samples than for the Slovanik samples.This means that the separation according to thenumber of PO units under ‘‘critical conditions’’ forthe EO block is possible in reversed-phase systemsfor Novanik sample types in mobile phases con-taining 70% or less acetonitrile, but is difficult toachieve for the Slovanik samples.

Eq. (7) also describes well the retention of theEO–PO block (co)oligomers in the normal-phasesystems on a Separon SGX Amine column in 2-propanol–n-hexane (Table 3) and in acetonitrile–water–dichloromethane (Table 5) mobile phases. In2-propanol–hexane mobile phases the retention (logk) of the two types of block (co)oligomers exhibits alinear increase with increasing number of polar EOunits (Fig. 4), the quadratic term with g in Eq. (7)EO

is negligible. On the other hand, the retention of(co)oligomers decreases with increasing number ofrelatively non-polar PO units, but this decrease ismuch less significant than the increase of retentionwith increasing number of EO units (Fig. 5). Thevalues of the oligomer selectivity for PO units, loga , are negative and an order of magnitude lowerPO

than the positive values of the oligomer selectivityfor EO units, log a (Table 3). Hence, the sepa-EO

ration according to the number of EO units underclose-to ‘‘critical elution conditions’’ for the POblock is principally possible over a wide range ofconcentrations of 2-propanol in the mobile phase,where the species with different numbers of PO units

Fig. 3. Dependencies of the retention factors, k, on the number ofare co-eluted in a common peak. However, thePO units, n , for the oligomers with 13 EO units (A) and on thePO

oligomer selectivity for the PO units (negative) innumber of EO units, n , for the oligomers with seven PO unitsEO

(B) in a Novanik sample, type (PO) –(EO) –(PO) . column: Novanik is approximately seven-times larger than them n m

Separon SGX C , mobile phase: acetonitrile–water (50:50) (1),18 selectivity for the PO units in Slovanik, so that in(60:40) (2), (70:30) (3), (80:20) (4), (90:10) (5), temperature: this chromatographic system ‘‘critical elution con-408C.

ditions’’ and separation according to the number ofEO units can be achieved for Slovanik type

significantly the retention behavior, as is discussed (co)oligomers only.below in more detail. The quadratic term with g can be neglected onlyPO

The retention either decreases or increases with for the (EO) –(PO) –(EO) (Slovanik) (co)oligom-n m n

increasing number of EO units, n , with both ers, but it is approximately four-times larger for theEO

Slovanik and Novanik (co)oligomers, but the effect (PO) –(EO) –(PO) (Novanik) (co)oligomersm n m

of the number of EO units on the retention is much whose log k versus n plots are significantly curvedPO

lower than with PO units and the oligomer selectivity (Table 3, Fig. 5A and B).



(PO) –(EO) –(PO) (Novanik) and (EO) –(PO) –(EO) (Slovanik) block copolymers on a Separon SGX Amine column in 2-propanol–m n m n m n2 2hexane mobile phases: log k5log b 1n log a 1n log g 1n log a 1n log gEO EO EO EO PO PO PO PO

Novanik 30% 2-Propanol Slovanik 30% 2-Propanol 10% 2-Propanol

Log b 0.3960.03 Log b 20.20060.005 0.25360.004Log a 0.08216 0.0004 Log a 0.12760.003 0.22360.002EO EO

Log a 20.15460.009 Log a 20.022260.0003 20.011960.0003PO PO

Log g 0.005960.0006 Log g 0.001560.0007 20.002460.0005PO POaC.D. 0.9983 C.D. 0.9985 0.9996


The retention of the EO–PO (co)oligomers on a stationary phase are better solvated by the mobileSeparon SGX Amine column in acetonitrile–water– phase more rich in water while the PO units moredichloromethane mobile phases increases with in- distant from the surface are better solvated by thecreasing number of EO units (Fig. 6) and with bulk mobile phase with a lower concentration ofdecreasing number of PO units (Fig. 7) and can be water.also adequately described by Eq. (7), whose parame- In the Novanik samples, the inner polar EO blockters are given in Table 5. In contrast to the other two contributes to the retention, but the PO end blocks ofchromatographic systems studied, the oligomer low polarities diminish the retention. The contribu-selectivities for both EO and PO units are significant tion of the EO units in the center of the inner blockso that ‘‘critical conditions’’ neither for PO nor for to the retention is higher than that of the EO unitsEO blocks are observed and peaks corresponding to close to and shielded by the PO end blocks (Fig.the two types of distribution are seriously overlapped 6B). The contribution of the PO units in the endat any mobile phase composition. This chromato- blocks close to the inner block to the decrease of thegraphic system shows some features found with retention is probably more significant than the effectnormal-phase systems and other typical for reversed- of more distant PO units, which are better solvatedphase retention behavior. The identification of the by the bulk mobile phase (Fig. 7A). In the Slovanikindividual species was possible only using APCI-MS samples, the EO units in the end blocks have betterdetection for the deconvolution of overlapped peaks access to the surface of the adsorbent and are(Fig. 8). possibly not affected by the inner PO block, oriented

The log k versus n plots for the (EO) –(PO) – towards the bulk mobile phase so that their retentionEO n m

(EO) (Slovanik) (co)oligomers and the log k versus is affected less significantly by the PO block thann

n plots for the (PO) –(EO) –(PO) (Novanik) with the Novanik samples and show more regularPO m n m

(co)oligomers are significantly curved as demon- contribution to the retention (Fig. 6A). The PO unitsstrated by the relatively high values of the quadratic in the inner non-polar block oriented into the bulkterms with g for Slovanik and with g for liquid phase also show more regular contribution toEO PO

Novanik samples (Table 5). In this chromatographic decreasing retention than the PO units in the endsystem, preferential adsorption of water on the blocks of the Novanik samples (Fig. 7B).bonded amino column occurs. Consequently, oligo- Like in RP system with aqueous acetonitrile, themeric units in different distances from the other block sequence in the (co)oligomers affects signifi-block can be solvated to different extent by the cantly the retention behavior in the NP systemsmobile phase components and their contributions to studied.the retention may differ. It can be assumed that theadsorbed individual species have the EO block(s) 4.3. Effect of the mobile phase on the retention oforiented towards the surface of the amino phase and the EO–PO block copolymersthe PO block(s) towards the less polar bulk mobilephase. The EO units close to the surface of the In reversed-phase systems, the effect of the con-


Fig. 5. Dependencies of the retention factors, k, on the number ofPO units, n , for the oligomers with 0–4 units in a SlovanikFig. 4. Dependencies of the retention factors, k, on the number of PO

sample, type (EO) –(PO) –(EO) , in 2-propanol–n-hexaneEO units, n , for the oligomers with 11–17 PO units in a n m nEO

(10:90), mobile phase A for the oligomers with 7–14 EO units inSlovanik sample, type (EO) –(PO) –(EO) , in 2-propanol–n-n m n

a Novanik sample, type (PO) –(EO) –(PO) , in 2-propanol–n-hexane (10:90), mobile phase A and for the oligomers with 5–10 m n m

hexane (30:70), mobile phase B. Normal-phase chromatographyPO units in a Novanik sample, type (PO) –(EO) –(PO) , inm n m

on a Separon SGX Amine column, temperature: 408C.2-propanol–n-hexane (30:70), mobile phase B. Normal-phasechromatography on a Separon SGX Amine column, temperature:408C.

(Novanik) (co)oligomers exhibits minimum retentionin 60% acetonitrile as the mobile phase.

centration of acetonitrile in the mobile phases on the In normal-phase systems with a Separon SGXretention is adequately described by Eq. (1) only for Amine column and 2-propanol–n-hexane mobilethe (EO) –(PO) –(EO) (Slovanik) (co)oligomers phases, the effect of the concentration of 2-propanoln m n

(Table 2). The retention of (PO) –(EO) –(PO) in the mobile phase should be described by them n m


Fig. 7. Dependencies of the retention factors, k, on the number ofFig. 6. Dependencies of the retention factors, k, on the number of PO units, n , for the oligomers with 8, 12 and 15 EO units in aPOEO units, n , for the oligomers with 4, 6, 8 and 10 PO units in aEO Novanik sample, type (PO) –(EO) –(PO) , in acetonitrile–m n mSlovanik sample, type (EO) –(PO) –(EO) , in acetonitrile–n m n water–dichloromethane (59.4:0.6:40), mobile phase A and forwater–dichloromethane (39.6:0.4:60), mobile phase A and for the oligomers with three EO units in a Slovanik sample, typethe oligomers with 14 PO units in a Novanik sample, type (EO) –(PO) –(EO) , in acetonitrile–water–dichloromethanen m n(PO) –(EO) –(PO) , in acetonitrile–water–dichloromethanem n m (69.3:0.7:30) (1), (59.4:0.6:40) (2), (49.5:0.5:50) (3) and(69.3:0.7:30) (1), (59.4:0.6:40) (2), (49.5:0.5:50) (3) and (39.6:0.4:60) (4), mobile phases B. Normal-phase chromato-(39.6:0.4:60) (4), mobile phases B. Normal-phase chromatog- graphy on a Separon SGX Amine column, temperature: 408C.raphy on a Separon SGX Amine column, temperature: 408C.

acetonitrile–water–dichloromethane mobile phasesthree-parameter Eq. (4), the parameters of which are (Table 5), the plots of log k versus the concentrationgiven in Table 4 for the (EO) –(PO) –(EO) of aqueous acetonitrile, w, are linear in agreementn m n

(Slovanik) (co)oligomers. with Eq. (3) only for the (PO) –(EO) –(PO)m n m

In the NP systems with Separon SGX Amine and (Novanik) (co)oligomers (Fig. 9). The dependence of


Fig. 8. Normal-phase separation of a (PO) –(EO) –(PO) type sample (Novanik) on a Separon SGX Amine (5 mm) column (15033.3m n m

mm I.D.) in acetonitrile–water–dichloromethane (69.3:0.7:30). Flow-rate: 0.5 ml /min; temperature: 408C; detection: APCI(1)-MS. (A)1 1Chromatographic peaks extracted for [M1H] ions with three PO units; numbers5n . (B) Chromatographic peaks extracted for [M1H]EO

ions with 11 EO units; numbers5n .PO


Table 4Constants of the dependences of the retention factors, k, of (EO) –(PO) –(EO) (Slovanik) block copolymers on the concentration ofn m n

22 2m2-propanol, w (%, v/v, ?10 ) on a Separon Amine column in 2-propanol–hexane mobile phases (10–25% 2-propanol): k5(a1bw)

n 50 n 51 n 52 n 53EO EO EO EO

a 21.2260.01 20.4360.03 20.43260.007 20.328060.0001b 14.060.1 7.060.2 5.5960.06 4.41360.002m 0.69960.008 1.2460.07 1.2260.04 1.41360.001

aC.D. 1.00 1.00 1.00 1.00a C.D.5Coefficient of determination.

the retention of the (EO) –(PO) –(EO) (Slovanik) four peak groups. Gradient-elution separation of an m n

(co)oligomers should be described by the three-pa- Novanik sample according to the number of PO unitsrameter Eq. (4) and the plots of log k versus the is shown in Fig. 11. The oligomer selectivity for theconcentration of aqueous acetonitrile, w, are sig- EO units for the samples with inner EO block is lownificantly curved (Fig. 10). The constants of Eq. (4) enough over a wide composition range of the mobilefor this NP system are listed in Table 6, together phase, so that it allows reversed-phase gradient-with the coefficients of determination demonstrating elution separation at close-to ‘‘critical elution con-a good fit to the experimental data. ditions’’. However, the oligomer selectivity for the

PO units in the (EO) –(PO) –(EO) (Slovanik)n m n

4.4. Effect of the sequence distribution on the (co)oligomers is high enough to preclude reversed-separation of the EO–PO block (co)oligomers phase separations of these products under ‘‘critical

elution conditions’’for the PO block.The (PO) –(EO) –(PO) (Novanik) (co)oligom- The (EO) –(PO) –(EO) (Slovanik) (co)oligom-m n m n m n

ers with inner EO block and PO end blocks can be ers can be separated according to the number of EOseparated according to the number of PO units in units in normal-phase systems on a Separon SGXreversed-phase systems on a Separon SGX C Amine column in 2-propanol–hexane mobile phases.18

column in acetonitrile–water mobile phases only. Like in reversed-phase chromatography of NovanikGradient elution is necessary to separate more than samples, the oligomer selectivity for the PO units for


(PO) –(EO) –(PO) (Novanik) and (EO) –(PO) –(EO) (Slovanik) block copolymers on a Separon SGX Amine column in acetonitrile–m n m n m n2 2water–dichloromethane mobile phases: log k5log b 1n log a 1n log g 1n log a 1n log gEO EO EO EO PO PO PO PO

Mobile phase: acetonitrile–water–dichloromethane

69.3:0.7:30 59.4:0.6:40 49.5:0.5:50 39.6:0.4:60

NovanikLog b 0.23660.008 0.33860.007 0.43760.008 0.5860.01Log a 0.018860.0001 0.021760.0001 0.024760.0001 0.031260.0001EO

Log a 20.08260.002 20.09760.002 20.10760.002 20.12160.003PO

Log g 0.002560.0002 0.003260.0001 0.003660.0001 0.004360.0002POaC.D. 0.9973 0.9982 0.9985 0.9992

SlovanikLog b 20.1560.02 20.1160.01 20.066 0.01 0.0160.01Log a 0.1560.01 0.15360.008 0.15860.008 0.18260.009EO

Log g 20.01760.002 20.01660.002 20.01560.002 20.02060.002EO

Log a 20.019760.0007 20.020360.0005 20.021160.0005 20.020660.0006POaC.D. 0.9816 0.9899 0.9925 0.9891



Fig. 9. Dependencies of the retention factors, k, of the oligomers Fig. 10. Dependencies of the retention factors, k, of the oligomerswith three PO units and 8, 10, 12 and 14 EO units (A) and with 12 with 14 PO units and 0–4 EO units (A) and with three EO unitsEO units and 2–5 PO units (B) in a (PO) –(EO) –(PO) type and 12–17 PO units (B) in a (EO) –(PO) –(EO) typem n m n m n

(Novanik) block copolymer sample, on the concentration, w (%, (Slovanik) block copolymer sample, on the concentration, w (%,22 22v /v, ?10 ) of aqueous acetonitrile (99% acetonitrile, 1% water) v /v, ?10 ) of aqueous acetonitrile (99% acetonitrile, 1% water)

in acetonitrile–water–dichloromethane mobile phases on a in acetonitrile–water–dichloromethane mobile phases on aSeparon SGX Amine column; temperature5408C. Separon SGX Amine column; temperature5408C.

the samples with inner PO block is very low and are eluted in the order of increasing number of EOallows baseline resolution of oligomers with different units and successful separation into seven peaks wasnumbers of EO units using gradient elution under obtained for Slovanik samples with a linear gradientvirtually ‘‘critical elution conditions’’. The oligomers from 10% to 25% 2-propanol in hexane in 25 min


Table 6Constants of the dependences of the retention factors, k, (PO) –(EO) –(PO) (Novanik) and (EO) –(PO) –(EO) (Slovanik) blockm n m n m n

copolymers with different numbers of oxyethylene, n and oxypropylene, n , repeat units on the concentration of aqueous acetonitrileEO PO2m(99% acetonitrile: 1% water) in mobile phases acetonitrile–water–dichioromethane on a Separon SGX Amine column: k5(a1bw)

Novanikn 57 n 59 n 510 n 511 n 512 n 513 n 514PO EO EO EO EO EO EO

a 21.060.1 20.9760.05 20.8060.02 20.7160.03 20.71760.008 20.6560.01b 3.460.2 3.0260.08 2.6260.03 2.3860.04 2.2460.01 2.0960.01m 0.4160.04 0.4060.03 0.4760.02 0.5060.03 0.466 0.01 0.5160.02

aC.D. 0.9998 0.9999 1.0000 0.9999 1.0000 1.0000

n 512 n 55 n 56 n 57 n 58 n 59 n 510EO PO PO PO PO PO PO

a 20.4460.03 20.5560.03 20.7160.03 21.0160.02 21.2260.05 21.7560.06b 1.5560.04 1.8960.03 2.3860.04 3.1660.04 3.8360.08 5.360.1c 0.6060.06 0.5560.04 0.5060.03 0.4260.01 0.4260.02 0.3760.01

aC.D. 0.9998 0.9999 0.9999 1.0000 1.0000 1.0000

Slovanikn 514 n 51 n 52 n 53 n 54PO EO EO EO EO

a 21864 24.060.4 22.760.1 21.360.3b 56611 1261 8.060.3 4.360.7m 0.2360.01 0.2860.01 0.27360.009 0.3860.07

aC.D. 0.9999 0.9999 1.0000 0.9990

n 53 n 512 n 513 n 514 n 515 n 516 n 517EO PO PO PO PO PO PO

a 21.660.2 22.3604 22760.1 23.4160.08 23.560.02 24.760.01b 5.060.4 6.860.8 8.060.3 10.060.2 10.660.5 13.960.3m 0.3260.03 0.2860.03 0.27360.009 0.25360.003 0.27460.008 0.25060.003

aC.D. 1.0000 0.9996 0.9999 1.0000 1.0000 1.0000a C.D.5Coefficient of determination.

Fig. 11. Gradient-elution reversed-phase separation of a (PO) –(EO) –(PO) type (co)oligomer sample (Novanik) on a Separon SGX Cm n m 18

(7 mm) column (15033.3 mm I.D.) with evaporative light scattering detection. Gradient 15–100% acetonitrile in water in 25 min.Flow-rate: 0.5 ml /min, temperature: 408C. Peaks correspond to the oligomers with 5–14 PO units.


(Fig. 12A). Each peak contains species with the same conditions’’ are usually observed at a very narrownumber of EO units, but various numbers of PO mobile phase composition range. The reversed-phaseunits. system with a C column and acetonitrile–water18

The oligomer selectivity for the PO units in the mobile phases and the normal-phase system with aproducts with the end PO blocks is significantly bonded amine column and propanol–hexane mobilehigher than for the samples with the inner PO block, phases in this work differ from the earlier systems inso that the individual oligomers in the (PO) – that the composition range of the mobile phasesm

(EO) –(PO) (Novanik) products are co-eluted in yielding ‘‘critical elution conditions’’ for EO or forn m

normal-phase systems on the bonded Amine column PO units in the block EO–PO (co)oligomers is veryin 2-propanol–hexane mobile phases (Fig. 12B). broad, which makes possible the application of

In the HPLC of (co)oligomers, the ‘‘critical elution gradient elution at the ‘‘critical elution conditions’’.

Fig. 12. Gradient-elution normal-phase separation of samples of block (co)oligomers on a Separon SGX Amine (5 mm) column (15033.3mm I.D.) with evaporative light scattering detection. Gradient 10–30% 2-propanol in n-hexane in 30 min. Flow-rate: 0.5 ml /min,temperature: 408C. (A) (EO) –(PO) –(EO) type sample (Slovanik); peaks correspond to the oligomers with 0–6 EO units; (B)n m n

(PO) –(EO) –(PO) type sample (Novanik); oligomers with 6–18 EO units and 5–10 PO units.m n m


However, the sequence distribution of the individual units. For the separation according to the number ofblocks in the (co)oligomers controls whether the the repeat units in the inner block, peak deconvolu-‘‘critical elution conditions’’ can be achieved or not. tion and reconstruction of the chromatograms usingThe present results suggest that the separation ac- HPLC–MS with APCI can be used. As an alternativecording to the number of repeat units in the end approach, two-dimensional HPLC techniques can beblocks at the ‘‘critical elution conditions’’ for the used for the separation according to the bimodalinner block units can be achieved, but such sepa- repeat units distribution, which is being presentlyration is not feasible for the products with the investigated.opposite block sequence. This can be possibly ex-plained by the conformation of the (co)oligomers, inwhich the end blocks are better exposed to the Acknowledgementsinteractions with the surface of the stationary phase,whereas direct interactions of the units in the inner This research was supported by the Grant Agencyblock are partially sterically hindered by the outer of Czech Republic, project 203/98/0598, and by theblocks. Ministry of Education of the Czech Republic, project

The oligomers in both (EO) –(PO) –(EO) VS 96058.n m n

(Slovanik) and (PO) –(EO) –(PO) (Novanik)m n m

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Retention mechanism, isocratic and gradient-elution ...distribution, liquid chromatography under...

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